I would probably use a repeated measures GLM for this which will allow you to better model your situation. But we use the tools we are familiar with so if you feel comfortable with MANCOVA and the assumptions, it's probably a good choice. As far as power, there are lots of options on that one. I've retired so not sure what the best available is to date. If you do go with MANCOVA, I think PASS has a subroutine for that...again, I'm out of the loop at this point.

For your 2 × 2 (Group × Time) design with two correlated DVs and three covariates, you have a few solid options:

=> Repeated-Measures MANCOVA

It's a multivariate ANCOVA with one within-subjects factor (Time: pre vs. post) + one between-subjects factor (Exposure: Greenspace vs. Urbanspace), + your three covariates. -> Simultaneously tests whether the time × group interaction differs on your two attentional‐control tasks, adjusting for covariates. [Thus, it controls Type I error by modeling the two DVs together + Accounts for the correlation between tasks + Adjusts for pre-existing differences via covariates (e.g., baseline mood, age, trait attention)].

On SPSS Software >> Analyze → General Linear Model → Repeated Measures >

> Define within-subject factor "Time" with two levels

> Add your two task scores as the Measure

> Add Exposure as a Between-Subjects factor

> Move covariates into the Covariate box

> Under Options → select "Time*Exposure" interaction, check "Adjust for covariates"

=> Two Separate ANCOVAs on Change Scores

In simple terms, it calculates a change score for each task: Δ = Post – Pre -> Run two between-subjects ANCOVAs (one per task), with Exposure as IV and your three covariates. [Thus, it's simpler to set up if you're less comfortable with multivariate GLMs & easier to interpret marginal means for each task. But -> You will lose the power benefit of modeling both DVs jointly, and you inflate Type I error unless you adjust (e.g., Bonferroni). However, I generally won't choose it when I've a more robust option..

=> Linear Mixed-Effects Models (LMEM)

Here, you treat Time as a repeated measure nested within Subject, Exposure as a fixed effect, Covariates as fixed predictors, and Subject as a random intercept (and possibly random slope for Time). [Thus, it handles missing data flexibly under MAR assumptions + Let's you model individual trajectories (random slopes) + Easily extendable to more time points or complex variance structures.]

On R Software >> Fit two separate LMEMs (one per task), or a multivariate LMEM in R's mlm or brms packages.

Which one to choose?

= If your primary goal is a simultaneous test of both tasks and you want to control familywise error -> go with Repeated-Measures MANCOVA.

= If you prefer simpler models and are okay interpreting each task separately -> use ANCOVA on change scores (with a Bonferroni or Holm correction).

= If you anticipate missing data or want to model individual differences in change -> choose LMEM.

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Regarding your question about the G*Power Analysis. It's unclear whether you're asking about a different software (such as PASS, StatsDirect, Epi_Info, etc) or a different statistical strategy (such as Monte Carlo Power Analysis, Precision Analysis, Bayesian Design Analysis, etc).

In general, for RM-MANCOVA, some recommend ≥ 20 observations per cell as a bare minimum, more if you have multiple covariates (to estimate parameters reliably) -> Look at published effect sizes in greenspace or attention studies to inform a more empirical guess for power.

I'd avoid MANCOVA and go for one of these options:

1. Regression with centred pre-score and centred covariates and categorical IV predicting each DV in a separate model. Possibly the easiest to interpret.

2. SEM with attentional control as a latent variable derived from your two DVs with with centred pre-score and centred covariates and categorical IV in a regression model.

3. Multivariate regression (not MANCOVA) predicting your two correlated DVs from centred pre-score and centred covariates and categorical IV in a regression model.

The issues with MAN(C)OVA are summarised here:

http://psychologicalstatistics.blogspot.com/2021/08/i-will-not-ever-never-run-manova.html

The main one is that the DV in MANOVA and MANCOVA is atheoretical and rarely interpretable or comparable between studies or analyses.